To celebrate the 50th anniversary of the New York Mycological Society and the 100th birthday of the composer John Cage, its founder, there will be an exhibition on mushrooms and Mr. Cage’s passion for them on Sept. 7 and 8 at the Cooper Union, 7 East Seventh Street (Third Avenue). Admission is free. On Sept. 8 from 8 to 11 p.m. there will be a performance of some of Mr. Cage’s works with film and photographic backdrops about mushrooms. Tickets benefit the society: $20 to $100, $5 for students, for the show. A pre-performance dinner at the home of the author Eugenia Bone is $200 a person, including the show, or $350 for two, from newyorkmyc.org.